Marlin Smith is a foreign exchange dealer with Investec South Africa. He notices the following quotes:

Spot exchange rate ZAR$1\mathrm{.}3220/$BWP

$1$ year forward exchange rate ZAR$1\mathrm{.}1492/$BWP

$1$ year BWP interest rate $5\mathrm{.}00\%$ per year

$1$ year ZAR interest rate $7\mathrm{.}50\%$ per year

$($a$)$ Calculate whether interest rate parity holds. You may ignore transaction costs. $(5)$

$($b$)$ With the aid of calculations from $($a$)$ above, show whether or not an arbitrage opportunity exists. $(3)$

$($c$)$ In the event that there is an arbitrage opportunity, you are required to demonstrate all the steps that need to be taken to make an arbitrage profit. Assume that Marlin Smith is authorised to work with BWP$1000000$ in the Botswana Pula market, or ZAR$1322000$ in the South African Rand market. Compute the arbitrage profit. $(12)$

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